Reverse Percentage Calculator — Find the Original Value
A reverse percentage calculation works backwards from a known result. If you know a value after it increased or decreased by a percentage, this calculator finds the original value. You can also find the whole number when you know that one number represents a particular percentage of it.
Find the original value before a percentage increase.
The common mistake
How to Calculate a Reverse Percentage
The most common mistake with reverse percentages is simply subtracting the percentage from the final value. That does not work, because the original percentage was calculated from the original value, not the final one.
A £100 item increased by 20% becomes £120. Reducing £120 by 20% gives £96 — not £100.
Why? The 20% increase was calculated from the original £100 (20% of £100 = £20). But a 20% decrease from £120 is calculated from the larger £120 base (20% of £120 = £24). The two percentages use different starting values, so they do not cancel out.
That is why reverse percentages require division rather than subtracting the percentage. To undo a 20% increase, divide by 1.20. To undo a 20% decrease, divide by 0.80. For day-to-day forward calculations, the Percentage Increase Calculator and Percentage Decrease Calculator do the opposite job to this page.
Reference
The three reverse percentage formulas
Original value before an increase
Original value = Final value ÷ (1 + percentage ÷ 100)
Example: £138 after a 15% increase → 138 ÷ 1.15 = £120.
Original value before a decrease
Original value = Final value ÷ (1 − percentage ÷ 100)
Example: £68 after a 15% decrease → 68 ÷ 0.85 = £80. The same logic recovers a pre-discount price — see the Discount Calculator for the forward direction.
Find the whole when you know a percentage
Whole = Known value ÷ (percentage ÷ 100)
Example: 45 is 30% of what? → 45 ÷ 0.30 = 150. This is the reverse of the basic Percentage Calculator.
See it in action
Worked examples
Find the original price before a 20% increase
- Final price: £120, increase: 20%
- Multiplier: 1 + (20 ÷ 100) = 1.20
- Original: 120 ÷ 1.20 = £100
Answer: £100
A price tag shows the post-increase figure and you need the original for a refund or comparison.
Find the original price before a 20% discount
- Sale price: £80, discount: 20%
- Multiplier: 1 − (20 ÷ 100) = 0.80
- Original: 80 ÷ 0.80 = £100
Answer: £100
Recovering the "was" price from a sale "now" price to check the advertised saving.
Find the original value before a 15% increase
- Final value: 230, increase: 15%
- Multiplier: 1 + (15 ÷ 100) = 1.15
- Original: 230 ÷ 1.15 = 200
Answer: 200
Reversing a metric that was reported after a 15% uplift, such as adjusted revenue or attendance.
Find the whole when 25 is 10%
- Known value: 25, percentage: 10%
- Decimal: 10 ÷ 100 = 0.10
- Whole: 25 ÷ 0.10 = 250
Answer: 250
A sample of 25 represents 10% of a population — find the total population size.
Find the original salary before a 5% pay rise
- New salary: £42,000, increase: 5%
- Multiplier: 1 + (5 ÷ 100) = 1.05
- Original: 42,000 ÷ 1.05 = £40,000
Answer: £40,000
You know the new salary after a 5% rise and need last year's figure for a comparison or application.
Answers
Frequently asked questions
What is a reverse percentage?
It means working backwards from a value that already includes a percentage increase, decrease or proportion. Instead of applying a percentage to find a result, you start with the result and recover the original.
How do I find the original number after a percentage increase?
Divide the final value by 1 plus the percentage as a decimal: Final ÷ (1 + percentage ÷ 100). £120 after a 20% rise is 120 ÷ 1.20 = 100.
How do I find the original number before a discount?
Divide the discounted price by 1 minus the discount as a decimal: Sale price ÷ (1 − discount ÷ 100). £80 after 20% off is 80 ÷ 0.80 = 100.
Why can't I just subtract the percentage?
Because the percentage was calculated from the original value, not the final one. A £100 item up 20% is £120, but 20% off £120 is £96 — not £100. The two percentages use different bases, so you must divide by the multiplier instead.
How do I find the number when I know X is Y percent of it?
Divide the known value by the percentage as a decimal: X ÷ (Y ÷ 100). If 30 is 20%, the whole is 30 ÷ 0.20 = 150.
Can reverse percentages be greater than 100%?
Percentage increases can exceed 100% — a 250% increase is reversed by dividing by 3.5. But a percentage decrease of 100% or more cannot be reversed into a unique finite original value, because 100% off leaves zero.
Can I use decimals?
Yes. Any decimal percentage works. £45 after a 12.5% increase is 45 ÷ 1.125 = 40, because 1 + 0.125 = 1.125.
Keep going
Related calculators
For the underlying rule behind every percentage question, read the How to Calculate Percentages guide.